Question

A man of mass $60\,{\text{kg}}$ climbs up a $20\,{\text{m}}$ long staircase to the top of a building $10\,{\text{m}}$ high. What is the work done by him? $\left( {{\text{Take g }} = {\text{ 1}}0{\text{ m}}\;{\text{s}} - {\text{2}}} \right)$.
(A) $12\,{\text{kJ}}$
(B) $6\,{\text{kJ}}$
(C) $3\,{\text{kJ}}$
(D) $18\,{\text{kJ}}$

Answer 1

Work is defined as the unit force applied on an object to move that object at unit distance. This question is asking about the work against gravity. Gravity points down and the acceleration of gravity which is given as $10$ multiplied by the mass of the man gives force. Multiply this force by the vertical distance and you have your answer. The $20$ meter length of the staircase is meaningless information to teach you the concept of path independence of work.

Complete step by step answer:
As we know that the work (where energy lost is taken as positive) is given by,
$\smallint {\text{Fds}}$
If we assume that there is only force of gravity and we only consider motion in one dimension (either with or against gravity), we come to the conclusion that $F = {\text{mg}}.$
Since we could say that we’re only considering motion with or against gravity, ${\text{ds}} = {\text{dh}}$ If we assume that the force of gravity doesn’t change as we change in height, or we consider it to be negligible
$\smallint Fds = F\Delta s$
$F = mg\Delta h$
Now we have all the terms we need.
We were told in the problem that the man’s mass is$60\,{\text{kg}}$ that gravitational field is ${\text{1}}0\,{\text{m}}/{{\text{s}}^{\text{2}}}\;$ and he climbed to the top of a $10\,{\text{m}}$high building, meaning that he changed his height by$10\,{\text{m}}$. I’ll take a moment to point out that they told you how long the staircase is, but that actually doesn’t matter. The only part that matters is the portion that’s against or with gravity, which is either up or down.
Hence,
$\Rightarrow W = mg\Delta h$
Now we will substitute the values,
$W = \left( {{\text{6}}0} \right)\left( {{\text{1}}0} \right)\left( {{\text{1}}0} \right){\text{ }}$
After simplification we will get,
$\Rightarrow W = {\text{6}}000{\text{J}}$
After converting the units, we will get,
$\therefore W = {\text{6}}\,{\text{kJ}}$

Thus, the correct option is B.

Note: We can solve this question in another way also. Multiply this force by the vertical distance and you have your answer. The $20$ meter length of the staircase is meaningless information to teach you the concept of path independence of work.